Unpolarized Nucleon Research Articles

Unpolarized transverse momentum dependent parton distributions of the nucleon from lattice QCD

We present a first lattice QCD calculation of the unpolarized nucleon’s isovector transverse-momentum-dependent parton distribution functions (TMDPDFs), which are essential to predict observables of multiscale, semi-inclusive processes in the standard model. We use a Nf=2+1+1 MILC ensemble with valence clover fermions on a highly improved staggered quark (HISQ) sea to compute the quark momentum distributions in a large-momentum nucleon on the lattice. The state-of-the-art techniques in renormalization and extrapolation in the correlation distance on the lattice are adopted. The perturbative kernel up to next-to-next-to-leading order is taken into account, and the dependence on the pion mass and the hadron momentum is explored. Our results are qualitatively comparable with phenomenological TMDPDFs, which provide an opportunity to predict high energy scatterings from first principles. Published by the American Physical Society 2024

Preliminary searches for spin-dependent interactions using sidebands of nuclear spin-precession signals.

Various theories beyond the Standard Model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A new P-odd and T-odd interaction between polarized and unpolarized nucleons proportional to s⃗⋅r̂ is one such possibility, where r⃗=rr̂ is the spatial vector connecting the nucleons, and s⃗ is the spin of the polarized nucleon. Such an interaction involving a scalar coupling gsN at one vertex and a pseudoscalar coupling gpn at the polarized nucleon vertex can be induced by the exchange of spin-0 pseudoscalar bosons. We describe a new technique to search for interactions of this form and present the first measurements of this type. We show that future improvements to this technique can improve the laboratory upper bound on the product gsNgpn by two orders of magnitude for interaction ranges at the 100 micron scale.

Search for an interaction mediated by axion-like particles with ultracold neutrons at the PSI

We report on a search for a new, short-range, spin-dependent interaction using a modified version of the experimental apparatus used to measure the permanent neutron electric dipole moment at the Paul Scherrer Institute. This interaction, which could be mediated by axion-like particles, concerned the unpolarized nucleons (protons and neutrons) near the material surfaces of the apparatus and polarized ultracold neutrons stored in vacuum. The dominant systematic uncertainty resulting from magnetic-field gradients was controlled to an unprecedented level of approximately 4 pT cm−1 using an array of optically-pumped cesium vapor magnetometers and magnetic-field maps independently recorded using a dedicated measurement device. No signature of a theoretically predicted new interaction was found, and we set a new limit on the product of the scalar and the pseudoscalar couplings m2 (95% C.L.) in a range of 5 µm mm for the monopole–dipole interaction. This new result confirms and improves our previous limit by a factor of 2.7 and provides the current tightest limit obtained with free neutrons.

New Limits on Exotic Spin-Dependent Interactions at Astronomical Distances.

Exotic spin-dependent interactions involving new light particles address key questions in modern physics. Interactions between polarized neutrons (n) and unpolarized nucleons (N) occur in three forms: g_{S}^{N}g_{P}^{n}σ·r, g_{V}^{N}g_{A}^{n}σ·v, and g_{A}^{N}g_{A}^{n}σ·v×r, where σ is the spin and g's are the corresponding coupling constants for scalar, pseudoscalar, vector, and axial-vector vertexes. If such interactions exist, the Sun and Moon could induce sidereal variations of effective fields in laboratories. By analyzing existing data from laboratory measurements on Lorentz and CPT violation, we derive new experimental upper limits on these exotic spin-dependent interactions at astronomical ranges. Our limits on g_{S}^{N}g_{P}^{n} surpass the previous combined astrophysical-laboratory limits, setting the most stringent experimental constraints to date. We also report new constraints on vector-axial-vector and axial-axial-vector interactions at astronomical scales, with vector-axial-vector limits improved by ∼12 orders of magnitude. We extend our analysis to Hari Dass interactions and obtain new constraints.

Improved Limits on an Exotic Spin- and Velocity-Dependent Interaction at the Micrometer Scale with an Ensemble-NV-Diamond Magnetometer.

Searching for exotic interactions provides a path for exploring new particles beyond the standard model. Here, we used an ensemble-NV-diamond magnetometer to search for an exotic spin- and velocity-dependent interaction between polarized electron spins and unpolarized nucleons at the micrometer scale. A thin layer of nitrogen-vacancy electronic spin ensemble in diamond is utilized as both the solid-state spin quantum sensor and the polarized electron source, and a vibrating lead sphere serves as the moving unpolarized nucleon source. The exotic interaction is searched by detecting the possible effective magnetic field induced by the moving unpolarized nucleon source using the ensemble-NV-diamond magnetometer. Our result establishes new bounds for the coupling parameter f_{⊥} within the force range from 5 to 400 μm. The upper limit of the coupling parameter at 100 μm is |f_{⊥}|≤1.1×10^{-11}, which is 3 orders of magnitude more stringent than the previous constraint. This result shows that NV ensemble can be a promising platform to search for hypothetical particles beyond the standard model.

Moments of the nucleon transverse quark spin densities using lattice QCD

We present the first calculation of the Mellin moments of the transverse quark spin densities in the nucleon using lattice QCD simulations with physical values of the pion mass and in the continuum limit. Specifically, we use three ${N}_{f}=2+1+1$ twisted mass fermion gauge ensembles each at different lattice spacings. The densities are extracted from the unpolarized and transversity generalized form factors. The first moment of transversely polarized quarks in an unpolarized nucleon shows an interesting distortion, which can be traced back to the sharp falloff of the transversity generalized form factor ${\overline{B}}_{Tn0}({Q}^{2})$. The isovector tensor anomalous magnetic moment is determined to be ${\ensuremath{\kappa}}_{T}=1.051(94)$, which confirms a negative and large Boer-Mulders function, ${h}_{1}^{\ensuremath{\perp}}$, in the nucleon.

Theory of deeply virtual Compton scattering off the unpolarized proton

Using the helicity amplitudes formalism, we study deeply virtual exclusive electron photoproduction off an unpolarized nucleon target, $ep\ensuremath{\rightarrow}{e}^{\ensuremath{'}}{p}^{\ensuremath{'}}\ensuremath{\gamma}$, through a range of kinematics both in the fixed target setting with initial electron energies of 6, 11, and 24 GeV and for an electron ion collider. We reformulate the cross section bringing to the forefront the defining features of the $ep\ensuremath{\rightarrow}{e}^{\ensuremath{'}}{p}^{\ensuremath{'}}\ensuremath{\gamma}$ process, where the observables are expressed as bilinear products of the independent helicity amplitudes which completely describe it in terms of the electric, magnetic, and axial currents of the nucleon. These contributions are checked against the Fourier harmonics-based formalism which has provided so far the underlying mathematical framework to study deeply virtual Compton scattering (DVCS) and related experiments. Using theoretical model calculations of the twist-two generalized parton distributions, $H$, $E$, $\stackrel{\texttildelow{}}{H}$, and $\stackrel{\texttildelow{}}{E}$, we uncover large discrepancies between the harmonic series and our proposed framework. Most importantly, these numerical differences appear in the intermediate ${Q}^{2}$ range which represents a sweet spot for extracting generalized parton distributions from data. We provide a framework that is ideal, on one side, to study and compare the different conventions that can be used to describe the leading order contribution to DVCS in QCD, while on the other it facilitates a quantitative extraction of physically meaningful information from experiment through traceable and controllable approximations in the intermediate ${Q}^{2}$ region.

Search for exotic spin-dependent interactions with a spin-based amplifier.

Development of new techniques to search for particles beyond the standard model is crucial for understanding the ultraviolet completion of particle physics. Several hypothetical particles are predicted to mediate exotic spin-dependent interactions between standard-model particles that may be accessible to laboratory experiments. However, laboratory searches are mostly conducted for static spin-dependent interactions, with a few experiments addressing spin- and velocity-dependent interactions. Here, we demonstrate a search for these interactions with a spin-based amplifier. Our technique uses hyperpolarized nuclear spins as an amplifier for pseudo-magnetic fields produced by exotic interactions by a factor of more than 100. Using this technique, we establish constraints on the spin- and velocity-dependent interactions between polarized neutrons and unpolarized nucleons for the force range of 0.03 to 100 meters, improving previous constraints by at least two orders of magnitude in partial force range. This technique can be further extended to investigate other exotic spin-dependent interactions.

Charged current electroproduction of a charmed meson at an electron-ion collider

We calculate the amplitude for exclusive electroweak production of a pseudoscalar ${D}_{s}$ or a vector ${D}_{s}^{*}$ charmed strange meson on an unpolarized nucleon, through a charged current, in leading order in ${\ensuremath{\alpha}}_{s}$. We work in the framework of the collinear QCD approach where generalized gluon distributions factorize from perturbatively calculable coefficient functions. We include both $O({m}_{c})$ terms in the coefficient functions and $O({M}_{D})$ mass term contributions in the heavy meson distribution amplitudes. We show that this process may be accessed at future electron-ion colliders.

Analytical perturbation theory and nucleon structure function in infrared region

We employ the analytic QCD (anQCD) approach to analyze the unpolarized nucleon structure function in deep inelastic scattering processes at next-to-leading-order accuracy. Considering the unreliable results of the underlying perturbative QCD (pQCD) at energy scales near to QCD cut off parameter ${Q}^{2}\ensuremath{\sim}{\mathrm{\ensuremath{\Lambda}}}^{2}$ and below, we modify the calculations at these scales using the anQCD approach and compare them with results from underlying pQCD and the available experimental data. The massive perturbation theory model is also used where an effective mass is attributed to gluons. Finally, we use the Jacobi polynomials formalism to transfer the calculations from Mellin moment space to Bjorken-$x$ space. To confirm the validity of the anQCD approach the Gottfried sum rule is also investigated. The achieved numerical results at low energy scales are compatible with what is expected and correspond to an admissible behavior of parton densities.

Search for an exotic parity-odd spin- and velocity-dependent interaction using a magnetic force microscope

Exotic spin-dependent interactions may be generated by exchanging hypothetical bosons that have been proposed to solve some mysteries in physics by theories beyond the standard model of particle physics. The search for such interactions can be conducted by tabletop scale experiments using high precision measurement techniques. Here we report an experiment to explore the parity-odd interaction between moving polarized electrons and unpolarized nucleons using a magnetic force microscope. The polarized electrons are provided by the magnetic tip at the end of a silicon cantilever, and their polarizations are approximately magnetized in the plane of the magnetic coating on the tip. A periodic structure with alternative gold and silicon dioxide stripes provides unpolarized nucleons with periodic number density modulation. The exotic forces are expected to change the oscillation amplitude of the cantilever which is measured by a fiber laser interferometer. Data has been taken by scanning the tip over the nucleon source structure at constant separation, and no exotic signal related to the density modulation has been observed. Thus, the experiment sets a limit on the electron-nucleon coupling constant, ${g}_{A}^{e}{g}_{V}^{N}\ensuremath{\le}9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ for $15\text{ }\text{ }\ensuremath{\mu}\mathrm{m}\ensuremath{\le}\ensuremath{\lambda}\ensuremath{\le}180\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, using a direct force measurement method.

Chiral Soliton Models and Nucleon Structure Functions

We outline and review the computations of polarized and unpolarized nucleon structure functions within the bosonized Nambu-Jona-Lasinio chiral soliton model. We focus on a consistent regularization prescription for the Dirac sea contribution and present numerical results from that formulation. We also reflect on previous calculations on quark distributions in chiral quark soliton models and attempt to put them into perspective.

Ultrasensitive optomechanical detection of an axion-mediated force based on a sharp peak emerging in probe absorption spectrum

Axion remains the most convincing solution to the strong-CP problem and a well-motivated dark matter candidate, causing the search for axions and axion-like particles(ALPs) to attract attention continually. The exchange of such particles may cause anomalous spin-dependent forces, inspiring many laboratory ALP searching experiments based on the detection of macroscopic monopole–dipole interactions between polarized electrons/nucleons and unpolarized nucleons. Since there is no exact proof of the existence of these interactions, to detect them is still of great significance. In the present paper, we study the electron–nucleon monopole–dipole interaction with a new method, in which a hybrid spin-nanocantilever optomechanical system consisting of a nitrogen-vacancy(NV) center and a nanocantilever resonator is used. With a static magnetic field and a pump microwave beam and a probe microwave beam applied, a probe absorption spectrum could be obtained. Through specific peaks appearing in the spectrum, we can identify this monopole–dipole interaction. And we also provide a prospective constraint to constrain the interaction. Furthermore, because our method can also be applied to the detection of some other spin-dependent interactions, this work provides new ideas for the experimental searches of the anomalous spin-dependent interactions.

Precision Measurement of the Beam-Normal Single-Spin Asymmetry in Forward-Angle Elastic Electron-Proton Scattering.

A beam-normal single-spin asymmetry generated in the scattering of transversely polarized electrons from unpolarized nucleons is an observable related to the imaginary part of the two-photon exchange process. We report a 2% precision measurement of the beam-normal single-spin asymmetry in elastic electron-proton scattering with a mean scattering angle of θ_{lab}=7.9° and a mean energy of 1.149GeV. The asymmetry result is B_{n}=-5.194±0.067(stat)±0.082 (syst) ppm. This is the most precise measurement of this quantity available to date and therefore provides a stringent test of two-photon exchange models at far-forward scattering angles (θ_{lab}→0) where they should be most reliable.

Constraints on the Velocity and Spin Dependent Exotic Interaction at the Micrometer Range.

We report on an experimental test of the velocity and spin dependent exotic interaction that can be mediated by new light bosons. The interaction is searched by measuring the force between a gold sphere and a microfabricated magnetic structure using a cantilever. The magnetic structure consists of stripes with antiparallel electron spin polarization so that the exotic interaction between the polarized electrons in the magnetic structure and the unpolarized nucleons in the gold sphere varies periodically, which helps to suppress the spurious background signals. The experiment sets the strongest laboratory constraints on the coupling constant between electrons and nucleons at the micrometer range with f_{⊥}<5.3×10^{-8} at λ=5 μm.

Probing the linearly polarized gluons in unpolarized proton with heavy-quark pair production

We consider the azimuthal cos φ and cos 2φ distributions and the Callan-Gross ratio R = dσL/dσT in heavy-quark pair electroproduction, , as probes of linearly polarized gluons in unpolarized nucleons. Our analysis shows that the azimuthal asymmetries and Callan-Gross ratio are predicted to be large and very sensitive to the contribution of the gluonic counterpart of the Boer-Mulders function, , describing the linear polarization of gluons inside unpolarized nucleon. In particular, the maximum values of the azimuthal distributions vary from 0 to 1 depending on . We conclude that future measurements of these quantities at the proposed EIC and LHeC colliders could clarify in details the proton spin decomposition puzzle.

Parton distribution functions from Ioffe time pseudo-distributions

In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution func- tions. We perform a systematic analysis using three lattice ensembles at two volumes, with lattice spacings a = 0.127 fm and a = 0.094 fm, for a pion mass of roughly 400 MeV. With two lattice spacings and two volumes, both continuum limit and infinite volume ex- trapolation systematic errors of the PDF are considered. In addition to the x dependence of the PDF, we compute their first two moments and compare them with the pertinent phenomenological determinations.

Experimental limit on an exotic parity-odd spin- and velocity-dependent interaction using an optically polarized vapor

Exotic spin-dependent interactions between fermions have recently attracted attention in relation to theories beyond the Standard Model. The exotic interactions can be mediated by hypothetical fundamental bosons which may explain several unsolved mysteries in physics. Here we expand this area of research by probing an exotic parity-odd spin- and velocity-dependent interaction between the axial-vector electron coupling and the vector nucleon coupling for polarized electrons. This experiment utilizes a high-sensitivity atomic magnetometer, based on an optically polarized vapor that is a source of polarized electrons, and a solid-state mass containing unpolarized nucleons. The atomic magnetometer can detect an effective magnetic field induced by the exotic interaction between unpolarized nucleons and polarized electrons. We set an experimental limit on the electron-nucleon coupling g_{mathrm{A}}^{mathrm{e}}g_{mathrm{V}}^{mathrm{N}} , < , 10^{ - 30} at the mediator boson mass below 10−4 eV, significantly improving the current limit by up to 17 orders of magnitude.

Experimental Constraint on an Exotic Spin- and Velocity-Dependent Interaction in the Sub-meV Range of Axion Mass with a Spin-Exchange Relaxation-Free Magnetometer.

We conducted a search for an exotic spin- and velocity-dependent interaction for polarized electrons with an experimental approach based on a high-sensitivity spin-exchange relaxation-free (SERF) magnetometer, which serves as both a source of polarized electrons and a magnetic-field sensor. The experiment aims to sensitively detect magnetic-fieldlike effects from the exotic interaction between the polarized electrons in a SERF vapor cell and unpolarized nucleons of a closely located solid-state mass. We report experimental results on the interaction with 82h of data averaging, which sets an experimental limit on the coupling strength around 10^{-19} for the axion mass m_{a}≲10^{-3} eV, within the important axion window.

N* Photoexcitation Results from Bonn

To investigate the excitation spectrum of the nucleons, photoproduction of mesons off polarized or unpolarized nucleons poses an ideal tool. The ELSA accelerator in Bonn provides electrons with energies up to 3.2 GeV, which can produce photon beams by bremsstrahlung off different radiator targets. Currently, there are two different experiments taking data: the BGO-OD and the CBELSA/TAPS experiment. Both are able to extract polarization observables for different final states, including charged and uncharged mesons. This contribution reports on the selection of different final states of both experiments and discusses the extracted observables. In addition, a truncated partial wave analysis is shown, which gives first insight into the sensitivity of the observables.